mvnplot: Graphical and Numerical Tests of Multivariate Normality for...

In davidaarmstrong/bsmds: Bootstrap Confidence Regions for Multidimensional Scaling Solutions

Description

This function implements the Friendly (1991) graphical test for multivariate normality on objects of class bsmds. It also provides numerical summaries (p-values) for tests of multivariate normality based on skewness and kurtosis as suggested by Kankainen et. al. (2007)

Usage

mvnplot(obj, sim.ci=TRUE, nreps=1000, num=FALSE, plot=TRUE, method="integration")

Arguments

obj	An object of class bsmds that contains bootstrap replicates for a multidimensional scaling solution.
sim.ci	Logical indicating whether simulated confidence bounds should be placed around the qq-plot.
nreps	The number of simulations to preform to calculate the confidence bounds.
num	Logical indicating whether numerical tests of multinormality should be calculated and presented
plot	Logical indicating whether the plot is to be printed
method	Method for calculating p-values, must be one of “integration”, “satterthwaite” or dQuotesimulation. See mvnorm.kur.test from the ICS package for more details.

Details

The Friendly (1991) graphical test plots the Mahalanobis distance between the bootstrap replications and the mean across the bootstrap replications against the quantiles of a chi-squared distribution with m (= number of dimensions in the multidimensional scaling solution) degrees of freedom. If the bootstrap replicates follow a multivariate normal distribution, the points in the figure should fall on the 45-degree line which is imposed on the plot. The details with respect to bootstrapped multidimensional scaling solutions are discussed in Jacoby and Armstrong (2011).

The numerical tests presented are the p-values from the mvnorm.kur.test and mvnorm.skew.test functions from the ICS package as discussed in Kankainen et. a.. (2007).

Value

plot	An xyplot object implementing the Friendly (1991) test
num	A numeric matrix of p-values from the two numerical tests for multinormality discussed above.

Author(s)

Dave Armstrong and William Jacoby

References

Friendly, M. 1991 SAS System for Statistical Graphics, 1st ed. SAS institute, Inc.

Jacoby, W.G. and D. Armstrong. 2011 Bootstrap Confidence Regions for Multidimensional Scaling Solutions. Unpublished Manuscript.

Kankainen, A., S. Taskinen and H. Oja 2007 Tests of Multinormality Based on Location Vectors and Scatter Matrices, Statistical Methods and Applications 16, 357–379.

Examples

data(thermometers2004)
out <- bsmds(thermometers2004, dist.fun = "dist", dist.data.arg = "x", 
	dist.args=list(method="euclidian"), R=25)
mvnplot(out, sim.ci=TRUE, nreps=1000, num=TRUE)

davidaarmstrong/bsmds documentation built on May 6, 2019, 8:32 p.m.